A038192 Bisection of A001317.

3, 15, 51, 255, 771, 3855, 13107, 65535, 196611, 983055, 3342387, 16711935, 50529027, 252645135, 858993459, 4294967295, 12884901891, 64424509455, 219043332147, 1095216660735, 3311419785987, 16557098929935, 56294136361779

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001317, A089893.

Programs

Mathematica

NestList[BitXor[2#,3#]&,3,30] (* Federico Provvedi, Sep 14 2023 *)

PARI

a(n)=sum(k=0, 2*n+1, (binomial(2*n+1, k)%2)<Charles R Greathouse IV, Aug 08 2013

PARI

A011371(n)=my(s);while(n>>=1,s+=n);s
A047999(n,k)=A011371(n)==A011371(k)+A011371(n-k)
a(n)=n+=n+1;sum(k=0, n, A047999(n, k)<Charles R Greathouse IV, Aug 09 2013

Python

def A038192(n): return sum((bool(~(m:=(n<<1)+1)&m-k)^1)<Chai Wah Wu, May 02 2023

Formula

a(n) = 12*A089893(n) + 3.

a(n+1) = (2 * a(n)) XOR (3 * a(n)), where XOR is the bitwise exclusive or operator. - Federico Provvedi, Sep 14 2023